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Business Mathematics Formulae

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  Business Mathematics Formulae 1.Arithmetic Mean a.Ungrouped data  x xnn totalnumberof dataelements == ∑ b.Weighted Mean wx xww weightalloted tothedataelement  == ∑∑ c.Grouped dataDirect Method int  fm xn f frequencym mid pon f totalof all frequencies ==== = ∑∑ Shortcut Method   fd  xAn Aarbitraryorassumedmean  ffrequencyddeviationofmidptfromassumedmeannftotalofallfrequencies = +==== = ∑∑ Step Deviation Method ''  fd  x A C n A arbitraryorassumed mean f frequencyd stepdowndeviationof mid pt fromassumed meanC stepdownmultiplen f totalof all frequencies = + ×===== = ∑∑ d.Combined Mean  1 1 2 2121 21 21 2 & 1& 2& 1& 2 n x n x xn n x x meansof group groupn n numberof elementsingroup group +=+== .!he M D#A$ a.Ungrouped Data 12 th n Forodd numberof items Valueof item Forevennumberof items Averagevalueof twomiddleitems +→→ b.Grouped Data 2 1112 ( )limlim12 l l  M l m c f   M medianl lower itof theclassinwhichmedianliesl upper itof theclassinwhichmedianlies f frequencyof themedianclassnmc cumulative frequencyof theclass preceding  −= + −====+== %.!he M&D Grouped Data 1 011 0 1 21102 ( ) ( )lim modmodmodmodint  f f   Mode l i f f f f  l lower itof classinwhich elies f frequencyof classinwhich elies f frequencyof class precedingthe alclass f frequencyof classsucceedingthe alclassi class erval  −= + ×− + −===== '.Geometric Mean 1 2 nn GMxxx = × ×−−−−− (.)armonic Mean Ungrouped Data  1 2 1 1 1 n n HM  x x x =+ +−−−−−−−−+ Grouped Data 1( ) ii n HM  f   x =× ∑ *.Mean Deviation Ungrouped Data | |  x x MDn −= Grouped Data | |  f d  MDn = ∑ +.Standard Deviation , -ariance Ungrouped Data 222 ( )( )  x xn x xn σ  σ   −=−= ∑∑ Simplied Formula /or Ungrouped Data 22222 iiii  x xn n x xn n σ  σ     = − ÷ ÷    = − ÷ ÷   ∑ ∑∑ ∑ Grouped Data 22 iiiiii  f x f x f f   σ     = − ÷ ÷   ∑ ∑∑ ∑ 0.Combined Standard Deviation  2 2 2 21 1 1 2 2 2121 2121 12 12 12 21 1 2 2121 2 ( ) ( ) n d n d n nCombined std devd x xd x xn x n x xn n σ σ  σ  σ   + + +=+== −= −+=+ .Coe2cient o/ -ariation 100% CV  x σ   = × 13. 4robabilit5 For mutuall5 e6clusive events ( ) ( ) ( )   Aor !  A  ! = + For non mutuall5 e6clusive events ( ) ( ) ( ) ( )   Aor !  A  !  Aand ! = + − #ndependent vents arg Pr ( )  M inal obability  A = intPr ( ) ( ) ( )   o obability A!  A  ! = × Pr ( / ) ( ) ( / ) ( ) Conditional obability A !  A or  ! A  ! = = Dependent vents arg Pr ( )Pr ( / ) ( )/ ( )( / ) ( )/ ( )intPr ( ) ( / )* ( )( ) ( / )* ( )  M inal obability  AConditional obability A !  A!  !  ! A  A!  A  o obability A!  A !  !  A!  ! A  A ===== Ba5es7 !heorem Let there be an event A, which can happen, only if one of the n  mutually exclusive events occur, then ( )  #umberof timeseventoccurs  event $otalnumberof occrances = 1 2 3, , , ....... n  ! ! ! ! ( ) ( / )( / )( ) ( / ) iiiii  !A! !A !A! = ∑
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